Readings Reflections
The readings reflections have two main purposes:
1) to hold you accountable for careful reading of and reflection on the readings assigned in class; and
2) to provide you with a record of what you've learned and thought about as a result of the readings.
The readings reflections will be evaluated using the following criteria:
completeness and timeliness of the entries;
comprehension of the main ideas of the readings; and
depth and quality of integration of the ideas with your own thinking.
Submit your readings reflection before reading anyone's on the Wiki page and then paste it into the existing reflection page for that current reading. This is due by Wed 9/14 at 11:58pm. In your reflection also indicate how the Communication Standard connects with the article or state why it doesn't connect at all!
Readings Discussions
This reading will also have a Wiki page discussion. The purpose of this is to engage in a conversation with your peers about the article, based on what you have written for your Readings Reflection. While you are not expected to read all of the reflections for each article, you are expected to read enough of them (after you have written yours so you are not unduly influenced) to be able to compare and contrast the thoughts of others with your thoughts about the article. Your contribution will be evaluated using the Math 3500 Online Readings Discussions Rubric handed out in class. The reading discussion will "close" for my examination by Sun 9/18 at 11:57pm.
The premise of this article is that student confidence and student involvement can both be increased through the implementation of cooperative learning in the classroom (6-3). As a result of this increased confidence and involvement, understanding will improve as well (6-3).
In cooperative learning, students work together to accomplish their goals, look for outcomes to benefit everyone, discuss ideas, and encourage one another (2-4). Furthermore, one study defines this concept as positive interdependence, individual accountability, equal participation, and simultaneous interaction (2-4). I find it interesting that cooperative learning is differentiated from group work (2-4). My initial reaction to reading the phrase “cooperative learning” was to label it as group work; however, the author chooses to refer to the students’ teams, instead of groups (3-1).
The author used her personal experience in the classroom and subsequent findings as the basis of the article. She described three groups of eighth grade students: high-ability, average, and low-ability (4-2), and detailed how a transition from the direct instruction model to cooperative learning caused these students to report that they felt more confident (4-5), more involved (5-5), and understood the mathematics better(6-2).
This article closely relates to the Communication Standard of the NCTM. Not only does the author mention trying to follow the NCTM standards within the first paragraph of the article, but it is also important to note that cooperative learning cannot take place without the necessary communication skills: explaining, justifying, etc. According to the standard, communication involves explaining one’s thinking about a problem to others in the class. Additionally, the Communication Standard says that teachers should facilitate a classroom environment in which communication is a key component of learning mathematics and evaluating what students know. The author of this article clearly incorporates these aspects into her implementation of cooperative learning.
Although she was doubtful about this cooperative learning model at the beginning, this teacher discovered that its implementation supported the many benefits of this style reported by others (6-3). These benefits include “higher academic achievement and social skills development”, “the development and growth of higher-level thinking skills, more frequent transfer of learned concepts to new situations, and more time on task”, among other aspects (2-5).Even though it was very difficult for this particular teacher to shift from a teacher-led environment to a cooperative learning classroom, she concluded that engaging in the struggle is well worth the benefits (6-4).
Like the author, I tend to be a bit skeptical of this cooperative learning approach, most likely because much of my educational experience has featured the traditional model of direct instruction. (Also, I believe that many others who have had a similar experience or have taught for a while may be hesitant to alter they way they teach.) However, I can se that when implemented well, this innovative approach can lead to significant classroom change and begin to develop middle school students into confident, involved individuals who have a much deeper comprehension of the mathematics curriculum than they would otherwise. Therefore, I hope to utilize this approach of cooperative learning in my future classroom.
Mandi Mills
Standing in front of a group of one’s peers and communicating ideas is difficult, even more so when the topic is not one in which the individual is confident. In order for mathematics classrooms to be transformed into spaces for thought-provoking mathematical discussion, students must build enough confidence in their abilities to be willing to share ideas and ask questions. NCTM points out that middle school classrooms present a special challenge for teachers trying to build a communicative atmosphere. The social norms of the middle school make any student reluctant to stand out, and as a result, “[…] students are self-conscious and hesitant to expose their thinking to others.” Fear of being marked as especially smart may prevent one student from sharing his or her thoughts, and students who fear being seen as lacking intelligence by their peers may hold back a discussion-provoking question. So how are we, as teachers, supposed to teach students to communicate their mathematical thinking effectively if the students are unwilling to practice this skill because of the potential for standing out?
In Nebesniak’s article, we read of one teacher’s effort to change her classroom into an environment that gives students the communication skills outlined by NCTM. She does this by giving her students a chance to actually converse about mathematical procedures. I feel that this is an important part of learning and understanding math. She described that this seemingly simple change was actually a radical shift from how her students previously learned mathematics. So much so, that she had to first teach the students how she expected them to learn before teaching them any subject content (3-2), which I feel would be necessary for the students’ understanding as they have most likely only learned math in a teacher-centered classroom. By grouping the students into teams, she built an atmosphere where students felt comfortable enough to share their work within these small groups. Speaking in front of the entire class may be intimidating, but speaking in front of a small group with which one is familiar takes some of the pressure of “standing out” away.
With this change, Nebesniak noticed that when difficult problems were presented, students no longer shied away from the task, (3-6) which she describes as a characteristic of active learners (4-3). When students were engaging with each other as well as the subject material, they can feel free to ask questions or try out a new idea. All the while they are increasing their understanding of the concept, and as a result of their understanding, their confidence grows. A teacher-centered learning environment doesn’t allow for students to have this kind of active engagement with the material. Their lack of engagement is what leads to their poor understanding and as a result, their decreased confidence in their abilities. Nebesniak’s students reported that they felt more confident when working in groups, (4-6) and the experience of working with their peers gave students a chance to practice fundamental mathematics communication skills. Her strategy is one that I would like to employ in the future as a teacher, because if we don’t allow students to converse with each other about their mathematical opinions and ideas, how can we expect them to ever take any real interest?
Valerie Gipper
The standard method of teacher led instruction has been drilled into all of us since the beginning of our career as lifelong students. This habit can be beneficial to the select few students who are engaged and have natural abilities surrounding mathematics. However, as evident in “Student Confidence and Student Involvement,” this method is not helpful for every student. In the article the author states that she struggles with how she feels her classroom should be ran and how it actually is being managed (1-2).
The author goes on to describe how difficult it is to implement a style of educating other than that of the traditional methods we are all used to. Fear of the unknown is something the other and I have in common. We both fear the lack of control that is inevitable when centering the classroom on student to student interaction (2-2). My fear is similar to that of Nebesniak, few students will complete the tasks promptly, and many students would copy work that was already completed, while others just socialized the whole time. (2-2)
This is where the difference between group work and cooperative learning really show. Johnson and Johnson define cooperative learning as, “Students work together to accomplish shared goals. Students seek outcomes that are beneficial to all. Students discuss material with each other, help one another understand it and encourage each other to work hard.” (2-4) This statement really struck a chord with me. I love the idea of students helping students. When a student can teach an idea or lesson to another student the student-teacher gets a better understanding of the material and the student will be more apt to ask for help next time. In both cases the students confidence is bolstered which can only lead to great things.
My goal as a future mathematics teacher is to pass on the confidence I have in myself to my students. In Nebesniak’s article she states that in her three classrooms comprised of students with varying abilities the majority, typically over eighty percent, of students benefited from the new structure of the classroom. These statistics are clearly shown in Figure four of the article. After the study was done and the students surveyed many if not most of the students stated that they gained a better understanding of the material when they were given a chance to work on it cooperatively with their peers.
Christopher Cardon
The article, “Student Confidence and Student Involvement,” is about a teacher reflecting on her teaching style, her days as a math student and how much she wants to change her current style of teaching but is not sure how. She longs for a more cooperative learning environment in her classroom even though she currently has been operating in a direct-instruction model as she had experienced throughout her years of schooling. I feel that cooperative learning environment is also extremely important in teaching. I too remember the days of simply sitting and listening to my teachers stand in front of me and lecturing. In my future classroom, I hope to find ways to get my students more involved and more hands on.
“Change is difficult. Changing an educator’s teaching style is perhaps one of the most difficult challenges in educational reform,” (Fennema and Nelson 1997; Fullan 2001) (98-2). This statement honestly scares me a bit. I think in order for us, as future teachers, to succeed in not resorting back to the “drill and kill” method, we need to have a goal of how we want to teach and study that method so we do not fall into the trap of teaching like so many of our previous teachers had done that we hated. I think the article makes it quite clear that we need to hit the ground running, and immediately implementing a different teaching style from day one.
The definition of cooperative learning and its benefits (98-4) – (98-7), discuss that cooperative learning is not simply group work. From the research presented in the article, it appears that cooperative learning can have a very powerful effect on students and it seems to definitely be for their benefit.
The ways of implementing cooperative learning in the classroom (98-8) – (99-1), seems to be achievable through many different models. In this respect, any teacher is sure to find a model that fits their views.
I think the communication standard ties to the article in a few ways. The standard discusses an example in which students work in pairs to solve a problem and this is what cooperative learning is about getting the students working together and talking. Also mentioned in the standard is the idea of students explaining their thinking, this relates to the article as well because in cooperative learning if one student has an idea they will need to be able to share that with whomever they are working with. Finally the third distinguishing feature discussed in the standard is the idea that teachers need to develop “a sense of community” so that students will feel more comfortable with one another which is same idea mentioned in the article.
Kaitlin Froehlke
Student confidence and involvement is so vital to the learning process. If students are not given a chance to feel self-worth or value in their interactions with material, then they will never really be involved in a great capacity. Creating an open environment where students feel safe and confident can be very difficult for teachers. Teachers are afraid of change and losing control of their classroom (2-2).
Students that are used to direct-instruction methods, and used to suppressing their immediate reactions and reflections in order to maintain a quiet learning atmosphere for the rest of the class, may have some trouble allowing themselves to react and behave more openly and outwardly with one another in a place where communication with one another is the norm. In small groups, as in cooperative learning, students work together, helping one another, bouncing ideas of each other, and giving one another confidence to succeed more so than in a traditional class wide session (3-1).
Students are given opportunities to explore the mathematics with one another and gain insight from other methods in their groups. Afterward students share their findings and are asked to justify their methods and results. In a classroom where feedback and sharing are norms, students can share ideas and when faced with questions or inquiries, they can show understanding by the ability to present and explain their method. The groups give more students a chance to participate. In the normal classroom setting the author describes her typical classroom participation, “the same five students wanted to answer the questions and the same ten students wanted to avoid them. (4-4)” But as cooperative learning was introduced students began to engage in a greater way, interacting with the task right away, when they used to take a lot longer to get focused and started. The majority of students responded that they had greater confidence when working with others (6-4).
Cooperative learning can provide students greater variations on learning environment and pace, I know as a student I always enjoyed a greater freedom as a student to work at a certain pace and explore mathematical ideas with peers. Following the group work, teams can be given the chance to present their material and help the rest of the class understand how they thought about the task and have their ideas challenged and questions, which forces them to have to justify steps taken. This would be difficult for students but it would definitely allow for a greater understanding of mathematical ideas and generalizations.
-kyle d.
Amy L. Nebesniak and Ruth M. Heaton, the two authors of the article we read, implemented the idea of cooperative learning within the classroom. This type of learning is a change from what students are used to and making that change happen is difficult (3-2). If I was trying to implement these changes into my own classroom, I think I would have many of the same reservations as that of the author’s. However, I do think cooperative learning, especially after reading this article, is a good idea for improving the students understanding of math. Cooperative learning is compiled of four principles: (1) positive interdependence, (2) individual accountability, (3) equal participation, and (4) simultaneous interaction (3-5). Each of these components is vitally important in creating an environment where the students can grow in their math abilities. It is also suggested these four items are the difference between group learning and cooperative learning (3-6). Actually making any program work in the classroom requires the teacher to fully believe it will work. They must be fully committed to teaching in this manner (3-9). This is true in anything you do though. If you are not confident it will work, there is no way anyone will believe you when you say it does. Once one has embraced the idea of cooperative learning, it is important to teach the students how it works as well (4-2). I see this as an important step in the whole process because if the students are not aware of what they are going to be doing as well as not prepared, the typical scenarios will ensue, as in one person doing all the work while others socialize and so on. One thing I found very interesting in this article was the three levels of math which were focused on, in particular the Core 3 class. Most people write off the students who have an issue learning math as unable to. However, as this article has shown, anyone can learn math and these so called “troubled” students were those who benefited the most from the cooperative learning program (7-fig. 4). Cooperative learning creates more interactive students (5-6). In any class where the teacher is the center and is simply lecturing the students, which is a situation I believe almost all of us have experienced, doesn’t allow us to interact with one another and the teacher. If we were to implement this idea of cooperative learning into our classes, understanding would be so much higher as well as the confidence of the students with their math. Confidence is one thing I really loved reading about in this article. I have worked with peers as well as students who thought they couldn’t do math because they were bad at it. They continually got wrong answers and were discouraged by this. Therefore they feel their math abilities were not up to par. The more students understand the math they are learning, the more confident they will become, as was shown by the data in the article (7-2). I think this is the key to improving our math classes. Communication within the cooperative learning is vitally important for the growth of the child. The teacher must communicate with the students telling them the instructions but not the answers. The students must communicate with one another during the problem solving process, working through problems. Also, the students must communicate their findings to the class and the teacher. This is an important step because being able to communicate how they got an answer is more important than the answer found. Sometimes students simply found the correct answer by guessing and checking. If students can easily communicate their process, they will gain the confidence they need. Katey Cook
Student Confidence and Student Involvement is about the struggles of changing to a cooperative learning setting from the normal (2-2) and the benefits of changing to such an approach (4-6). It is also important to note that even throughout their experience utilizing cooperative learning, it can still be an uncertain and challenging task (7-5).
The authors of the article, Amy Nebesniak and Ruth Heaton, discussed the desire to change from the normal use of direct instruction (2-2). In this, they discussed how the majority of their mathematical learning has come via direct instruction. While it is not surprising that most students have only been taught mathematics in that fashion, it is interesting to note that future math teachers have a difficult time breaking away from such methods.
The benefits of switching to cooperative instruction are outlined throughout the article. A vast majority of the students polled in the research study claim that their confidence is improved when working with a team (4-8). They also claim an increase of feeling involved in the classroom (5-10) and a greater understanding of mathematical concepts (7-3).
Even with the benefits outlined, I still would like to see more research data. Namely, I would like to see on how students taught through such an approach do on, as Problem Solving and Mathematical Beliefs puts it, mathematical exercises. Does this teaching approach lead to improved math skills as measured by state tests such as the MEAP? All signs point toward yes, but I would like to see such a study.
In relation to Communication Standards, I would say that Nebesniak and Heaton do strive towards a goal of increasing mathematical understanding, but it is not shown whether or not students are capable of discussing mathematics as outlined in Communication Standards. For all that is told in the article, it is safe to assume that some students can help other students (6-1), but can they describe the inner workings of a problem to the teacher? When they do cooperative learning, are they discussing mathematics and problem solving or are they showing each other how to plug numbers into a formula? In short, we are never shown the communication ability of the students. As this article is presented, Communication Standards are not clearly met.
-Marcus Edgette
The article entitled “Student Confidence and Student Involvement” walks us through a teacher’s use of cooperative learning and the results of utilizing this method of learning. The authors acknowledge that changing the classroom norms is very difficult for an educator (2-2). I would agree that change is very difficult to implement, especially if one is very stubborn, but can yield great results in increasing student engagement in the classroom.
The article goes on to define cooperative learning as students working together to accomplish the task at hand with the students serving as sounding boards and tutors for each other as they discuss the problems with one another and encourage each other to do their best (2-4). Some benefits that have been researched include higher academic achievement and social skills development (2-6). The teacher kept a journal and did team interviews to gage the progress of her students during the implementation of cooperative learning.
The results that she found were that the majority of students had more confidence in attacking problems in groups (4-5). Before the cooperative learning initiative the teacher claims that getting students to begin working on problems was quite a task, but with the cooperative learning students of all ability levels began working on problems immediately (4-6). She mentioned that before some students were somewhat hesitant to attack the problems assigned. As a substitute experience I have learned that students without confidence are very reluctant to attack problems. It is never a problem to get students to attack a problem if they are confident in their abilities in math. Cooperative learning increases the confidence of the students, which allows students to attack problems faster. From the teacher’s interviews with students we can see that they value the opinions of their peers, and appreciate having other minds to bounce ideas off of to make sure they obtain the correct solution (5-6).
The teacher also noticed that the cooperative learning helped to engage her students more actively. She said they communicated their engagement with their body language. They would interact with both their peers and the teacher (5-11). The active engagement led to more involvement and that leads to a better understanding of math. In order for cooperative learning to work students must be able to communicate their mathematical thinking through explanations to their team or partner. They will improve on this aspect as they get to know their group members and learn how to fully explain their logic. This aspect of cooperative learning aligns with the communication standard for grades 6-8 of NCTM.
Mike Freeland
Two things every educator strives to see come to life in their classroom are confidence and involvement. The article by Nebesniak and Heaton, “Student Confidence and Student Involvement” gives a depiction of the author’s struggle towards creating a cooperative classroom where students are involved and confident in their mathematical work. She mentioned a need to teach the kids what proper cooperation in her classroom looked like (4-1). Through her study she found that some of the positive outcomes of cooperative learning include higher academic achievement and well developed social skills (3-5), students with lower abilities felt more confident to try problems and work toward understanding in a cooperative environment (7-4), and that this style of instruction fosters confidence which can lead to increased understanding (4-4).
The author was only able to attempt a change in teaching style after changing school districts. Her new school district used curriculum that encouraged a cooperative environment (3-3). In my opinion, this was the best setting for her to be able to try a new teaching strategy and as new teachers it would be very valuable for us to figure out our own philosophy and desired teaching strategy before entering the field.
I find it discouraging that it wasn’t until after started taking graduate classes that she changed her view and it wasn’t until she changed school districts that she was able to apply her new knowledge “I gained important knowledge by listening to the different ways that my peers approached and solved problems,” (3-1).
The communication standards for grades 6-8 in the Principles & Standards for School Mathematics briefly state that students should be able to: organize and consolidate their thinking, communicate their thinking coherently, analyze and evaluate others, and effectively use mathematical language (267-1).
The most valuable thing I have been able to take from the standards section is the role of the teacher in student’s communication. They say that the teacher should establish norms that support the learning of all students, ask meaningful questions, and guide discussions that do arise (270-2). I believe her attempts to create a cooperative environment incorporate some of the communication standards; she even references them in the beginning of the article. In order to work cooperatively students must be able to employ the requirements of communicating their thoughts coherently and receptively analyze other students. Tori Ward
The “Student Confidence and Student involvement” article is about a teacher who implemented cooperative learning into her classroom. Once she was able to control the process, her students were more engaged and more willing to tackle difficult problems. In her past educational experiences and teacher preparation she had not been directly exposed to this teaching approach. The majority of her education beginning in elementary school and continuing through the postsecondary school operated on the direct instruction model. The first time she was able to see the incredible benefit of cooperative learning was in her grad class. There she was immersed in an atmosphere that expected participants to form partnerships with one another that deepened their individual understanding of math. She gained important knowledge by listening to the different ways that her peers approached and solved problems. When she explained problems to others, her own understanding of the mathematics increased. 98-1
The benefits of cooperative learning include higher academic achievement and social skills development. With these benefits their also comes a growth of higher level thinking skills, more frequent transfer of learned concepts to new situations and more time on task. 98-8 In order for her to put her cooperative learning practices into use she realized that her students needed to break free of traditional expectations and be taught what it meant to learn in a cooperative group. 99-1 She used Kagans team-building and class-building activities to create a “positive team identity, liking, respect, and trust among team members and classmates.” 99-2 Once students began to get to know one another the cooperation increased significantly. 99-2 She gathered a survey of students from classes in what she calls “high achieving, average and low achieving” and asks them questions about their confidence, math abilities, involvement and understanding in the math class when placed in groups. Roughly 3/4 of the students typically liked being in the groups better. It seems as though her rough start in begging turned out to have a good cause in the end.
The communication standard connects with article in several ways. It noted that kids are reluctant to do anything that causes them to stand out from the group, and many middle-grades students are self-conscious and hesitant to expose their thinking to others. 268-1. Teachers should build a sense of community in middle-grades classrooms so students feel free to express their ideas honestly and openly, without fear of ridicule.269-1. In the article the teacher also does this in using Kagans team-building and class-building activities to create a “positive team identity, liking, respect, and trust among team members and classmates.” 99-2 Once students began to get to know one another the cooperation increased significantly. In the communication standards it also says that teachers need to monitor students learning in order to direct classroom discourse appropriately. 271- 4. In the article as the teacher began to incorporate cooperative learning, the number of students who became more engaged in mathematics and with one another increased. Her role shifted from dispenser of mathematical knowledge to facilitator of mathematical conversations and understandings. 100-5
Gathering all this information makes me come to a conclusion that students have increased confidence in their mathematical abilities when working in cooperative learning teams. They have a higher thinking order which makes them be able to solve harder and challenging problems. Me as a future should take notes on these studies for i have also foster the idea of cooperative learning so I can see my students accelerate in mathematics.
Fredrick Martin
Student Confidence and Student Involvement is written by a teacher that is having difficulty with implementing an idea she is interested in trying into her classroom both out of the fear and difficulty that comes with change and being unsure if it will have a positive affect on the students learning of the material. Cooperative learning can be very difficult, especially for students of middle school age and even more so if it is not something that is done on a consistent basis. As the communication standard said, children of that age don’t want to stick out by appearing particularly bright or very stupid. From my own experience I must agree that was definitely something I went through. Because of this it is important that if “cooperative learning” is going to be put into use, it must be a near everyday thing so that the students can become comfortable with those around them and wont hesitate to correct, help, ask for help and just generally share ideas. As the article pointed out, "Once students began to get to know one another, the cooperation increased significantly.” (4-2) Another benefit I feel comes from this sort of environment is that students would likely become more open to asking questions, because as they work together in groups they are likely to find that someone in their group has the same question a lot of the time, so asking it feels less embarrassing than when everyone is working individually and the teaching is lecturing. The article seemed to agree with this when it cited the surveys of the students saying that working in groups made participation in math class easier. This is also backed by the author’s observation, “Before implementing cooperative learning groups, student involvement in my classes was sporadic. No matter what teaching technique I tried, the same five students wanted to answer the questions and the same ten students wanted to avoid them. As I began to incorporate cooperative learning, the number of students who became more engaged in mathematics and with one another increased.” (5-9)
Along with these things I feel this sort of interactive environment would help the students become more accepting of their own abilities and those around them. Someone who is particularly gifted in math will be able to help the other students in the class, so rather than possibly being resented by his or her classmates, they may actually appreciate his or her abilities. At the same time a student that needs a bit more help may feel less embarrassed and worried because he or she would be able to see that the almost every kid in the class has problems with some topic at some point, and that by asking for help they’re able to pick up on a lot more things than they would have been able to otherwise.
-Doug Wills
I believe as teachers we will want to do what it is that has been traditionally done, automatically repeat what was done when we were in school by teaching the traditionally way of operating on the direct-instruction model (97,2). We all obviously want to teach our students in the best possible learning experience that we can. For some this may work for them on learning the mathematics, but this will not be the majority of the students, and they will probably be only memorizing rules like what was mentioned in our last reading. Cooperative learning does sound great, but as mentioned it is a challenge and very difficult to do (98,2). I concur that in order for this to work, and be able to teach this way in your school, all your co-workers have to believe in it and teaching the same way in their classrooms (98,3). Teaching is a team effort, and everyone has to buy into what you are doing in order to succeed in anything that you do, and teaching is no different. All that we want is for our students to understand math, and enjoy what it is that they are doing. As seen in this study, students are not only succeeding in math, but enjoying it and being able to get more out of what they are being taught.
Students are also more confident with mathematics (100,7), and when you are having confidence in something you will want to do more of it. This is a critical age level in life, because if you fail in something or not confident in doing something then you will want to easily give up with it and not pursue it anymore in life. Math is something that everyone uses every day, and the more that people know about math and can be able to help others out.
With letting the students work together in groups/teams they learn to better explain their ways, because in smaller groups you get a better participation from everyone. This also helps with shifting from the teacher always explaining everything to the students to students teaching each other (100,9).
Teaching this way will always be a learning process for us (102,5). Until this is happening as a standard in every school and that generation of students come around to being teachers, this is always going to be a struggle since were never taught this way and changes are always a challenge.
Bret Van Zanten
It seems to me that in this article it seems as though Nebesniak and Heaton wants to inform the reader about cooperative learning over all. I however think that going into so much detail about cooperative learning was a bit redundant. The redundancy I’m experiencing may be from having taken the education classes and knowing what cooperative learning is about. If student confidence is our goal then I agree that cooperative learning can help accomplish that. When we make cooperative groups in the manner intend for them then we get the desired result however when we just group students then we get groups that may not work because they don’t know what cooperative learning is supposed to be and what a cooperative group member is and isn’t supposed to do (2-2). While the article reflects on how to build confidence through cooperative student lead learning by going through one teachers experience and different methods of study it also makes it so that we as future teachers reflect on what exactly builds student confidence.
In order to build student confidence we must make that student feel as they could do that problem or handle any situation that may be thrown their way. The authors do this through frequent prompting for core 3, answering the questions of the core two and allowing the core one class to be free to work (4-5). Not only that but allowing the students to feel as though they are in it together throughout the process so they are less intimidated by their vast knowledge or the lack there of. We also learn that the students feel as though they always have support that allows them to feel more confident (5-4). In my honest opinion this helps students in so many ways but they may never realize it unless you point it out to them.
When I think of student confidence it makes me realize that even now I am not confident in my abilities when I am in the role of a student. However when I am assuming the role of a teacher then I know I can encourage the kids to do well and work together because I know what it feels like to be uncertain of whether or not I’m doing something right. Whenever I am with classmate I can see and hear what the other students are thinking. This way I can know if I am completely off base when it comes to a certain problem. In a way this article allows me to consider what kinds of teaching applies to make students more confident and thus more able to communicate their ideas. If we can make a student confident enough to speak out in class then we can make our jobs as teachers easier because it would be easier to assess those who are less willing to participate in class for lack of confidence.
Denise Slate
__
Cooperative learning may be challenging to implement, but proves to be an effective teaching method in “Student Confidence and Student Involvement” (4-6). Through cooperative learning, students have the opportunity to explore different techniques when solving problems. There is strength in numbers, and working together as a team gives students more confidence in experimenting with new techniques and enables them to learn from their mistakes (3-8).
Confidence in math is still something I struggle with (MATH 3140 confirmed this). It takes courage to delve into a problem without fully understanding the proper technique to solve it. Especially when there is that prowling possibility that you may end up with a wrong answer (3-5). For a student to develop this confidence, teachers should encourage students, at a young age, to try a variety of strategies. If a student makes a mistake, have that student reflect on it, maybe even write a journal entry about it. Ultimately, they will learn from their mistakes and build confidence in the process. This article did convince me that cooperative learning is effective for all students, but I can’t help but wonder how much input the less confident students put into these team activities? I believe that implementing the reflection of mistakes and incorporating it with cooperative learning could help even the quieter students gain the confidence to speak up more within their teams.
The Communication Standards go hand-in-hand with this article. The concept of peers communicating with each other to solve a problem is at the core of cooperative learning. The standards for communication mention organizing, communicating, analyzing, and evaluating mathematical thoughts (1-1). Cooperative learning helps students meet these standards.
Hailey McDonell
Before reading this article on cooperative learning I already established expectations of what I would learn: how much more students learn, how much easier they learn, and how much they enjoy learning cooperatively. This is not the first class attempting to introduce the idea of cooperative, self-regulated learning. Every time I am lectured on alternate styles of teaching I skeptically listen, waiting to hear how we are expected to implement such a new, unstructured style. The current method, I imagine, is to stand in front of the class for a majority of the time lecturing in front of the board, and feed students as much as you can in an hour. Although most of us grew up learning this way, now we are told that this method is not the way to go. But it seemed so efficient and easy?
By now I know that allowing students to work collaboratively on math will mix up the class a little bit and provide alternate methods of learning, but how would I expect to have time for both lecture and independent/group work? This article suggests that collaborative learning will actually save time for students and teachers, and after reading I understood how. Authors Amy Nebesniak and Ruth Heaton accurately describe my past learning experiences: the teacher lectures a topic to the class, then provides an assignment; high achieving students start on tasks right away, the average students (me) would slowly get to work after a few questions are answered, and the low-ability students would struggle, require frequent individual attention and “reteaching.” That sounds more time consuming, for a majority of the class, than allowing students to work together in a structured environment.
I am still reluctant to rely completely on cooperative learning, worried that students may waist or misuse the time I give them. But if I find a structure I like, similar to the way the author of the article did, and it yields good results, than I would integrate that system more and more into my classroom as my comfort allows. Hopefully my first attempt will go better than I expect, then the transformation of my classroom will occur quicker, benefitting more of my students as well as myself.
The readings reflections have two main purposes:
1) to hold you accountable for careful reading of and reflection on the readings assigned in class; and
2) to provide you with a record of what you've learned and thought about as a result of the readings.
The readings reflections will be evaluated using the following criteria:
- completeness and timeliness of the entries;
- comprehension of the main ideas of the readings; and
- depth and quality of integration of the ideas with your own thinking.
Submit your readings reflection before reading anyone's on the Wiki page and then paste it into the existing reflection page for that current reading. This is due by Wed 9/14 at 11:58pm. In your reflection also indicate how the Communication Standard connects with the article or state why it doesn't connect at all!Readings Discussions
This reading will also have a Wiki page discussion. The purpose of this is to engage in a conversation with your peers about the article, based on what you have written for your Readings Reflection. While you are not expected to read all of the reflections for each article, you are expected to read enough of them (after you have written yours so you are not unduly influenced) to be able to compare and contrast the thoughts of others with your thoughts about the article. Your contribution will be evaluated using the Math 3500 Online Readings Discussions Rubric handed out in class. The reading discussion will "close" for my examination by Sun 9/18 at 11:57pm.
The premise of this article is that student confidence and student involvement can both be increased through the implementation of cooperative learning in the classroom (6-3). As a result of this increased confidence and involvement, understanding will improve as well (6-3).
In cooperative learning, students work together to accomplish their goals, look for outcomes to benefit everyone, discuss ideas, and encourage one another (2-4). Furthermore, one study defines this concept as positive interdependence, individual accountability, equal participation, and simultaneous interaction (2-4). I find it interesting that cooperative learning is differentiated from group work (2-4). My initial reaction to reading the phrase “cooperative learning” was to label it as group work; however, the author chooses to refer to the students’ teams, instead of groups (3-1).
The author used her personal experience in the classroom and subsequent findings as the basis of the article. She described three groups of eighth grade students: high-ability, average, and low-ability (4-2), and detailed how a transition from the direct instruction model to cooperative learning caused these students to report that they felt more confident (4-5), more involved (5-5), and understood the mathematics better(6-2).
This article closely relates to the Communication Standard of the NCTM. Not only does the author mention trying to follow the NCTM standards within the first paragraph of the article, but it is also important to note that cooperative learning cannot take place without the necessary communication skills: explaining, justifying, etc. According to the standard, communication involves explaining one’s thinking about a problem to others in the class. Additionally, the Communication Standard says that teachers should facilitate a classroom environment in which communication is a key component of learning mathematics and evaluating what students know. The author of this article clearly incorporates these aspects into her implementation of cooperative learning.
Although she was doubtful about this cooperative learning model at the beginning, this teacher discovered that its implementation supported the many benefits of this style reported by others (6-3). These benefits include “higher academic achievement and social skills development”, “the development and growth of higher-level thinking skills, more frequent transfer of learned concepts to new situations, and more time on task”, among other aspects (2-5).Even though it was very difficult for this particular teacher to shift from a teacher-led environment to a cooperative learning classroom, she concluded that engaging in the struggle is well worth the benefits (6-4).
Like the author, I tend to be a bit skeptical of this cooperative learning approach, most likely because much of my educational experience has featured the traditional model of direct instruction. (Also, I believe that many others who have had a similar experience or have taught for a while may be hesitant to alter they way they teach.) However, I can se that when implemented well, this innovative approach can lead to significant classroom change and begin to develop middle school students into confident, involved individuals who have a much deeper comprehension of the mathematics curriculum than they would otherwise. Therefore, I hope to utilize this approach of cooperative learning in my future classroom.
Mandi Mills
Standing in front of a group of one’s peers and communicating ideas is difficult, even more so when the topic is not one in which the individual is confident. In order for mathematics classrooms to be transformed into spaces for thought-provoking mathematical discussion, students must build enough confidence in their abilities to be willing to share ideas and ask questions. NCTM points out that middle school classrooms present a special challenge for teachers trying to build a communicative atmosphere. The social norms of the middle school make any student reluctant to stand out, and as a result, “[…] students are self-conscious and hesitant to expose their thinking to others.” Fear of being marked as especially smart may prevent one student from sharing his or her thoughts, and students who fear being seen as lacking intelligence by their peers may hold back a discussion-provoking question. So how are we, as teachers, supposed to teach students to communicate their mathematical thinking effectively if the students are unwilling to practice this skill because of the potential for standing out?
In Nebesniak’s article, we read of one teacher’s effort to change her classroom into an environment that gives students the communication skills outlined by NCTM. She does this by giving her students a chance to actually converse about mathematical procedures. I feel that this is an important part of learning and understanding math. She described that this seemingly simple change was actually a radical shift from how her students previously learned mathematics. So much so, that she had to first teach the students how she expected them to learn before teaching them any subject content (3-2), which I feel would be necessary for the students’ understanding as they have most likely only learned math in a teacher-centered classroom. By grouping the students into teams, she built an atmosphere where students felt comfortable enough to share their work within these small groups. Speaking in front of the entire class may be intimidating, but speaking in front of a small group with which one is familiar takes some of the pressure of “standing out” away.
With this change, Nebesniak noticed that when difficult problems were presented, students no longer shied away from the task, (3-6) which she describes as a characteristic of active learners (4-3). When students were engaging with each other as well as the subject material, they can feel free to ask questions or try out a new idea. All the while they are increasing their understanding of the concept, and as a result of their understanding, their confidence grows. A teacher-centered learning environment doesn’t allow for students to have this kind of active engagement with the material. Their lack of engagement is what leads to their poor understanding and as a result, their decreased confidence in their abilities. Nebesniak’s students reported that they felt more confident when working in groups, (4-6) and the experience of working with their peers gave students a chance to practice fundamental mathematics communication skills. Her strategy is one that I would like to employ in the future as a teacher, because if we don’t allow students to converse with each other about their mathematical opinions and ideas, how can we expect them to ever take any real interest?
Valerie Gipper
The standard method of teacher led instruction has been drilled into all of us since the beginning of our career as lifelong students. This habit can be beneficial to the select few students who are engaged and have natural abilities surrounding mathematics. However, as evident in “Student Confidence and Student Involvement,” this method is not helpful for every student. In the article the author states that she struggles with how she feels her classroom should be ran and how it actually is being managed (1-2).
The author goes on to describe how difficult it is to implement a style of educating other than that of the traditional methods we are all used to. Fear of the unknown is something the other and I have in common. We both fear the lack of control that is inevitable when centering the classroom on student to student interaction (2-2). My fear is similar to that of Nebesniak, few students will complete the tasks promptly, and many students would copy work that was already completed, while others just socialized the whole time. (2-2)
This is where the difference between group work and cooperative learning really show. Johnson and Johnson define cooperative learning as, “Students work together to accomplish shared goals. Students seek outcomes that are beneficial to all. Students discuss material with each other, help one another understand it and encourage each other to work hard.” (2-4) This statement really struck a chord with me. I love the idea of students helping students. When a student can teach an idea or lesson to another student the student-teacher gets a better understanding of the material and the student will be more apt to ask for help next time. In both cases the students confidence is bolstered which can only lead to great things.
My goal as a future mathematics teacher is to pass on the confidence I have in myself to my students. In Nebesniak’s article she states that in her three classrooms comprised of students with varying abilities the majority, typically over eighty percent, of students benefited from the new structure of the classroom. These statistics are clearly shown in Figure four of the article. After the study was done and the students surveyed many if not most of the students stated that they gained a better understanding of the material when they were given a chance to work on it cooperatively with their peers.
Christopher Cardon
The article, “Student Confidence and Student Involvement,” is about a teacher reflecting on her teaching style, her days as a math student and how much she wants to change her current style of teaching but is not sure how. She longs for a more cooperative learning environment in her classroom even though she currently has been operating in a direct-instruction model as she had experienced throughout her years of schooling. I feel that cooperative learning environment is also extremely important in teaching. I too remember the days of simply sitting and listening to my teachers stand in front of me and lecturing. In my future classroom, I hope to find ways to get my students more involved and more hands on.
“Change is difficult. Changing an educator’s teaching style is perhaps one of the most difficult challenges in educational reform,” (Fennema and Nelson 1997; Fullan 2001) (98-2). This statement honestly scares me a bit. I think in order for us, as future teachers, to succeed in not resorting back to the “drill and kill” method, we need to have a goal of how we want to teach and study that method so we do not fall into the trap of teaching like so many of our previous teachers had done that we hated. I think the article makes it quite clear that we need to hit the ground running, and immediately implementing a different teaching style from day one.
The definition of cooperative learning and its benefits (98-4) – (98-7), discuss that cooperative learning is not simply group work. From the research presented in the article, it appears that cooperative learning can have a very powerful effect on students and it seems to definitely be for their benefit.
The ways of implementing cooperative learning in the classroom (98-8) – (99-1), seems to be achievable through many different models. In this respect, any teacher is sure to find a model that fits their views.
I think the communication standard ties to the article in a few ways. The standard discusses an example in which students work in pairs to solve a problem and this is what cooperative learning is about getting the students working together and talking. Also mentioned in the standard is the idea of students explaining their thinking, this relates to the article as well because in cooperative learning if one student has an idea they will need to be able to share that with whomever they are working with. Finally the third distinguishing feature discussed in the standard is the idea that teachers need to develop “a sense of community” so that students will feel more comfortable with one another which is same idea mentioned in the article.
Kaitlin Froehlke
Student confidence and involvement is so vital to the learning process. If students are not given a chance to feel self-worth or value in their interactions with material, then they will never really be involved in a great capacity. Creating an open environment where students feel safe and confident can be very difficult for teachers. Teachers are afraid of change and losing control of their classroom (2-2).
Students that are used to direct-instruction methods, and used to suppressing their immediate reactions and reflections in order to maintain a quiet learning atmosphere for the rest of the class, may have some trouble allowing themselves to react and behave more openly and outwardly with one another in a place where communication with one another is the norm. In small groups, as in cooperative learning, students work together, helping one another, bouncing ideas of each other, and giving one another confidence to succeed more so than in a traditional class wide session (3-1).
Students are given opportunities to explore the mathematics with one another and gain insight from other methods in their groups. Afterward students share their findings and are asked to justify their methods and results. In a classroom where feedback and sharing are norms, students can share ideas and when faced with questions or inquiries, they can show understanding by the ability to present and explain their method. The groups give more students a chance to participate. In the normal classroom setting the author describes her typical classroom participation, “the same five students wanted to answer the questions and the same ten students wanted to avoid them. (4-4)” But as cooperative learning was introduced students began to engage in a greater way, interacting with the task right away, when they used to take a lot longer to get focused and started. The majority of students responded that they had greater confidence when working with others (6-4).
Cooperative learning can provide students greater variations on learning environment and pace, I know as a student I always enjoyed a greater freedom as a student to work at a certain pace and explore mathematical ideas with peers. Following the group work, teams can be given the chance to present their material and help the rest of the class understand how they thought about the task and have their ideas challenged and questions, which forces them to have to justify steps taken. This would be difficult for students but it would definitely allow for a greater understanding of mathematical ideas and generalizations.
-kyle d.
Amy L. Nebesniak and Ruth M. Heaton, the two authors of the article we read, implemented the idea of cooperative learning within the classroom. This type of learning is a change from what students are used to and making that change happen is difficult (3-2). If I was trying to implement these changes into my own classroom, I think I would have many of the same reservations as that of the author’s. However, I do think cooperative learning, especially after reading this article, is a good idea for improving the students understanding of math.
Cooperative learning is compiled of four principles: (1) positive interdependence, (2) individual accountability, (3) equal participation, and (4) simultaneous interaction (3-5). Each of these components is vitally important in creating an environment where the students can grow in their math abilities. It is also suggested these four items are the difference between group learning and cooperative learning (3-6).
Actually making any program work in the classroom requires the teacher to fully believe it will work. They must be fully committed to teaching in this manner (3-9). This is true in anything you do though. If you are not confident it will work, there is no way anyone will believe you when you say it does. Once one has embraced the idea of cooperative learning, it is important to teach the students how it works as well (4-2). I see this as an important step in the whole process because if the students are not aware of what they are going to be doing as well as not prepared, the typical scenarios will ensue, as in one person doing all the work while others socialize and so on.
One thing I found very interesting in this article was the three levels of math which were focused on, in particular the Core 3 class. Most people write off the students who have an issue learning math as unable to. However, as this article has shown, anyone can learn math and these so called “troubled” students were those who benefited the most from the cooperative learning program (7-fig. 4). Cooperative learning creates more interactive students (5-6). In any class where the teacher is the center and is simply lecturing the students, which is a situation I believe almost all of us have experienced, doesn’t allow us to interact with one another and the teacher. If we were to implement this idea of cooperative learning into our classes, understanding would be so much higher as well as the confidence of the students with their math.
Confidence is one thing I really loved reading about in this article. I have worked with peers as well as students who thought they couldn’t do math because they were bad at it. They continually got wrong answers and were discouraged by this. Therefore they feel their math abilities were not up to par. The more students understand the math they are learning, the more confident they will become, as was shown by the data in the article (7-2). I think this is the key to improving our math classes.
Communication within the cooperative learning is vitally important for the growth of the child. The teacher must communicate with the students telling them the instructions but not the answers. The students must communicate with one another during the problem solving process, working through problems. Also, the students must communicate their findings to the class and the teacher. This is an important step because being able to communicate how they got an answer is more important than the answer found. Sometimes students simply found the correct answer by guessing and checking. If students can easily communicate their process, they will gain the confidence they need.
Katey Cook
Student Confidence and Student Involvement is about the struggles of changing to a cooperative learning setting from the normal (2-2) and the benefits of changing to such an approach (4-6). It is also important to note that even throughout their experience utilizing cooperative learning, it can still be an uncertain and challenging task (7-5).
The authors of the article, Amy Nebesniak and Ruth Heaton, discussed the desire to change from the normal use of direct instruction (2-2). In this, they discussed how the majority of their mathematical learning has come via direct instruction. While it is not surprising that most students have only been taught mathematics in that fashion, it is interesting to note that future math teachers have a difficult time breaking away from such methods.
The benefits of switching to cooperative instruction are outlined throughout the article. A vast majority of the students polled in the research study claim that their confidence is improved when working with a team (4-8). They also claim an increase of feeling involved in the classroom (5-10) and a greater understanding of mathematical concepts (7-3).
Even with the benefits outlined, I still would like to see more research data. Namely, I would like to see on how students taught through such an approach do on, as Problem Solving and Mathematical Beliefs puts it, mathematical exercises. Does this teaching approach lead to improved math skills as measured by state tests such as the MEAP? All signs point toward yes, but I would like to see such a study.
In relation to Communication Standards, I would say that Nebesniak and Heaton do strive towards a goal of increasing mathematical understanding, but it is not shown whether or not students are capable of discussing mathematics as outlined in Communication Standards. For all that is told in the article, it is safe to assume that some students can help other students (6-1), but can they describe the inner workings of a problem to the teacher? When they do cooperative learning, are they discussing mathematics and problem solving or are they showing each other how to plug numbers into a formula? In short, we are never shown the communication ability of the students. As this article is presented, Communication Standards are not clearly met.
-Marcus Edgette
The article entitled “Student Confidence and Student Involvement” walks us through a teacher’s use of cooperative learning and the results of utilizing this method of learning. The authors acknowledge that changing the classroom norms is very difficult for an educator (2-2). I would agree that change is very difficult to implement, especially if one is very stubborn, but can yield great results in increasing student engagement in the classroom.
The article goes on to define cooperative learning as students working together to accomplish the task at hand with the students serving as sounding boards and tutors for each other as they discuss the problems with one another and encourage each other to do their best (2-4). Some benefits that have been researched include higher academic achievement and social skills development (2-6). The teacher kept a journal and did team interviews to gage the progress of her students during the implementation of cooperative learning.
The results that she found were that the majority of students had more confidence in attacking problems in groups (4-5). Before the cooperative learning initiative the teacher claims that getting students to begin working on problems was quite a task, but with the cooperative learning students of all ability levels began working on problems immediately (4-6). She mentioned that before some students were somewhat hesitant to attack the problems assigned. As a substitute experience I have learned that students without confidence are very reluctant to attack problems. It is never a problem to get students to attack a problem if they are confident in their abilities in math. Cooperative learning increases the confidence of the students, which allows students to attack problems faster. From the teacher’s interviews with students we can see that they value the opinions of their peers, and appreciate having other minds to bounce ideas off of to make sure they obtain the correct solution (5-6).
The teacher also noticed that the cooperative learning helped to engage her students more actively. She said they communicated their engagement with their body language. They would interact with both their peers and the teacher (5-11). The active engagement led to more involvement and that leads to a better understanding of math. In order for cooperative learning to work students must be able to communicate their mathematical thinking through explanations to their team or partner. They will improve on this aspect as they get to know their group members and learn how to fully explain their logic. This aspect of cooperative learning aligns with the communication standard for grades 6-8 of NCTM.
Mike Freeland
Two things every educator strives to see come to life in their classroom are confidence and involvement. The article by Nebesniak and Heaton, “Student Confidence and Student Involvement” gives a depiction of the author’s struggle towards creating a cooperative classroom where students are involved and confident in their mathematical work. She mentioned a need to teach the kids what proper cooperation in her classroom looked like (4-1). Through her study she found that some of the positive outcomes of cooperative learning include higher academic achievement and well developed social skills (3-5), students with lower abilities felt more confident to try problems and work toward understanding in a cooperative environment (7-4), and that this style of instruction fosters confidence which can lead to increased understanding (4-4).
The author was only able to attempt a change in teaching style after changing school districts. Her new school district used curriculum that encouraged a cooperative environment (3-3). In my opinion, this was the best setting for her to be able to try a new teaching strategy and as new teachers it would be very valuable for us to figure out our own philosophy and desired teaching strategy before entering the field.
I find it discouraging that it wasn’t until after started taking graduate classes that she changed her view and it wasn’t until she changed school districts that she was able to apply her new knowledge “I gained important knowledge by listening to the different ways that my peers approached and solved problems,” (3-1).
The communication standards for grades 6-8 in the Principles & Standards for School Mathematics briefly state that students should be able to: organize and consolidate their thinking, communicate their thinking coherently, analyze and evaluate others, and effectively use mathematical language (267-1).
The most valuable thing I have been able to take from the standards section is the role of the teacher in student’s communication. They say that the teacher should establish norms that support the learning of all students, ask meaningful questions, and guide discussions that do arise (270-2). I believe her attempts to create a cooperative environment incorporate some of the communication standards; she even references them in the beginning of the article. In order to work cooperatively students must be able to employ the requirements of communicating their thoughts coherently and receptively analyze other students.
Tori Ward
The “Student Confidence and Student involvement” article is about a teacher who implemented cooperative learning into her classroom. Once she was able to control the process, her students were more engaged and more willing to tackle difficult problems. In her past educational experiences and teacher preparation she had not been directly exposed to this teaching approach. The majority of her education beginning in elementary school and continuing through the postsecondary school operated on the direct instruction model. The first time she was able to see the incredible benefit of cooperative learning was in her grad class. There she was immersed in an atmosphere that expected participants to form partnerships with one another that deepened their individual understanding of math. She gained important knowledge by listening to the different ways that her peers approached and solved problems. When she explained problems to others, her own understanding of the mathematics increased. 98-1
The benefits of cooperative learning include higher academic achievement and social skills development. With these benefits their also comes a growth of higher level thinking skills, more frequent transfer of learned concepts to new situations and more time on task. 98-8 In order for her to put her cooperative learning practices into use she realized that her students needed to break free of traditional expectations and be taught what it meant to learn in a cooperative group. 99-1 She used Kagans team-building and class-building activities to create a “positive team identity, liking, respect, and trust among team members and classmates.” 99-2 Once students began to get to know one another the cooperation increased significantly. 99-2 She gathered a survey of students from classes in what she calls “high achieving, average and low achieving” and asks them questions about their confidence, math abilities, involvement and understanding in the math class when placed in groups. Roughly 3/4 of the students typically liked being in the groups better. It seems as though her rough start in begging turned out to have a good cause in the end.
The communication standard connects with article in several ways. It noted that kids are reluctant to do anything that causes them to stand out from the group, and many middle-grades students are self-conscious and hesitant to expose their thinking to others. 268-1. Teachers should build a sense of community in middle-grades classrooms so students feel free to express their ideas honestly and openly, without fear of ridicule.269-1. In the article the teacher also does this in using Kagans team-building and class-building activities to create a “positive team identity, liking, respect, and trust among team members and classmates.” 99-2 Once students began to get to know one another the cooperation increased significantly. In the communication standards it also says that teachers need to monitor students learning in order to direct classroom discourse appropriately. 271- 4. In the article as the teacher began to incorporate cooperative learning, the number of students who became more engaged in mathematics and with one another increased. Her role shifted from dispenser of mathematical knowledge to facilitator of mathematical conversations and understandings. 100-5
Gathering all this information makes me come to a conclusion that students have increased confidence in their mathematical abilities when working in cooperative learning teams. They have a higher thinking order which makes them be able to solve harder and challenging problems. Me as a future should take notes on these studies for i have also foster the idea of cooperative learning so I can see my students accelerate in mathematics.
Fredrick Martin
Student Confidence and Student Involvement is written by a teacher that is having difficulty with implementing an idea she is interested in trying into her classroom both out of the fear and difficulty that comes with change and being unsure if it will have a positive affect on the students learning of the material. Cooperative learning can be very difficult, especially for students of middle school age and even more so if it is not something that is done on a consistent basis. As the communication standard said, children of that age don’t want to stick out by appearing particularly bright or very stupid. From my own experience I must agree that was definitely something I went through. Because of this it is important that if “cooperative learning” is going to be put into use, it must be a near everyday thing so that the students can become comfortable with those around them and wont hesitate to correct, help, ask for help and just generally share ideas. As the article pointed out, "Once students began to get to know one another, the cooperation increased significantly.” (4-2)
Another benefit I feel comes from this sort of environment is that students would likely become more open to asking questions, because as they work together in groups they are likely to find that someone in their group has the same question a lot of the time, so asking it feels less embarrassing than when everyone is working individually and the teaching is lecturing. The article seemed to agree with this when it cited the surveys of the students saying that working in groups made participation in math class easier. This is also backed by the author’s observation, “Before implementing cooperative learning groups, student involvement in my classes was sporadic. No matter what teaching technique I tried, the same five students wanted to answer the questions and the same ten students wanted to avoid them. As I began to incorporate cooperative learning, the number of students who became more engaged in mathematics and with one another increased.” (5-9)
Along with these things I feel this sort of interactive environment would help the students become more accepting of their own abilities and those around them. Someone who is particularly gifted in math will be able to help the other students in the class, so rather than possibly being resented by his or her classmates, they may actually appreciate his or her abilities. At the same time a student that needs a bit more help may feel less embarrassed and worried because he or she would be able to see that the almost every kid in the class has problems with some topic at some point, and that by asking for help they’re able to pick up on a lot more things than they would have been able to otherwise.
-Doug Wills
I believe as teachers we will want to do what it is that has been traditionally done, automatically repeat what was done when we were in school by teaching the traditionally way of operating on the direct-instruction model (97,2). We all obviously want to teach our students in the best possible learning experience that we can. For some this may work for them on learning the mathematics, but this will not be the majority of the students, and they will probably be only memorizing rules like what was mentioned in our last reading. Cooperative learning does sound great, but as mentioned it is a challenge and very difficult to do (98,2). I concur that in order for this to work, and be able to teach this way in your school, all your co-workers have to believe in it and teaching the same way in their classrooms (98,3). Teaching is a team effort, and everyone has to buy into what you are doing in order to succeed in anything that you do, and teaching is no different. All that we want is for our students to understand math, and enjoy what it is that they are doing. As seen in this study, students are not only succeeding in math, but enjoying it and being able to get more out of what they are being taught.
Students are also more confident with mathematics (100,7), and when you are having confidence in something you will want to do more of it. This is a critical age level in life, because if you fail in something or not confident in doing something then you will want to easily give up with it and not pursue it anymore in life. Math is something that everyone uses every day, and the more that people know about math and can be able to help others out.
With letting the students work together in groups/teams they learn to better explain their ways, because in smaller groups you get a better participation from everyone. This also helps with shifting from the teacher always explaining everything to the students to students teaching each other (100,9).
Teaching this way will always be a learning process for us (102,5). Until this is happening as a standard in every school and that generation of students come around to being teachers, this is always going to be a struggle since were never taught this way and changes are always a challenge.
Bret Van Zanten
It seems to me that in this article it seems as though Nebesniak and Heaton wants to inform the reader about cooperative learning over all. I however think that going into so much detail about cooperative learning was a bit redundant. The redundancy I’m experiencing may be from having taken the education classes and knowing what cooperative learning is about. If student confidence is our goal then I agree that cooperative learning can help accomplish that. When we make cooperative groups in the manner intend for them then we get the desired result however when we just group students then we get groups that may not work because they don’t know what cooperative learning is supposed to be and what a cooperative group member is and isn’t supposed to do (2-2). While the article reflects on how to build confidence through cooperative student lead learning by going through one teachers experience and different methods of study it also makes it so that we as future teachers reflect on what exactly builds student confidence.
In order to build student confidence we must make that student feel as they could do that problem or handle any situation that may be thrown their way. The authors do this through frequent prompting for core 3, answering the questions of the core two and allowing the core one class to be free to work (4-5). Not only that but allowing the students to feel as though they are in it together throughout the process so they are less intimidated by their vast knowledge or the lack there of. We also learn that the students feel as though they always have support that allows them to feel more confident (5-4). In my honest opinion this helps students in so many ways but they may never realize it unless you point it out to them.
When I think of student confidence it makes me realize that even now I am not confident in my abilities when I am in the role of a student. However when I am assuming the role of a teacher then I know I can encourage the kids to do well and work together because I know what it feels like to be uncertain of whether or not I’m doing something right. Whenever I am with classmate I can see and hear what the other students are thinking. This way I can know if I am completely off base when it comes to a certain problem. In a way this article allows me to consider what kinds of teaching applies to make students more confident and thus more able to communicate their ideas. If we can make a student confident enough to speak out in class then we can make our jobs as teachers easier because it would be easier to assess those who are less willing to participate in class for lack of confidence.
Denise Slate
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Cooperative learning may be challenging to implement, but proves to be an effective teaching method in “Student Confidence and Student Involvement” (4-6). Through cooperative learning, students have the opportunity to explore different techniques when solving problems. There is strength in numbers, and working together as a team gives students more confidence in experimenting with new techniques and enables them to learn from their mistakes (3-8).
Confidence in math is still something I struggle with (MATH 3140 confirmed this). It takes courage to delve into a problem without fully understanding the proper technique to solve it. Especially when there is that prowling possibility that you may end up with a wrong answer (3-5). For a student to develop this confidence, teachers should encourage students, at a young age, to try a variety of strategies. If a student makes a mistake, have that student reflect on it, maybe even write a journal entry about it. Ultimately, they will learn from their mistakes and build confidence in the process. This article did convince me that cooperative learning is effective for all students, but I can’t help but wonder how much input the less confident students put into these team activities? I believe that implementing the reflection of mistakes and incorporating it with cooperative learning could help even the quieter students gain the confidence to speak up more within their teams.
The Communication Standards go hand-in-hand with this article. The concept of peers communicating with each other to solve a problem is at the core of cooperative learning. The standards for communication mention organizing, communicating, analyzing, and evaluating mathematical thoughts (1-1). Cooperative learning helps students meet these standards.
Hailey McDonell
Before reading this article on cooperative learning I already established expectations of what I would learn: how much more students learn, how much easier they learn, and how much they enjoy learning cooperatively. This is not the first class attempting to introduce the idea of cooperative, self-regulated learning. Every time I am lectured on alternate styles of teaching I skeptically listen, waiting to hear how we are expected to implement such a new, unstructured style. The current method, I imagine, is to stand in front of the class for a majority of the time lecturing in front of the board, and feed students as much as you can in an hour. Although most of us grew up learning this way, now we are told that this method is not the way to go. But it seemed so efficient and easy?
By now I know that allowing students to work collaboratively on math will mix up the class a little bit and provide alternate methods of learning, but how would I expect to have time for both lecture and independent/group work? This article suggests that collaborative learning will actually save time for students and teachers, and after reading I understood how. Authors Amy Nebesniak and Ruth Heaton accurately describe my past learning experiences: the teacher lectures a topic to the class, then provides an assignment; high achieving students start on tasks right away, the average students (me) would slowly get to work after a few questions are answered, and the low-ability students would struggle, require frequent individual attention and “reteaching.” That sounds more time consuming, for a majority of the class, than allowing students to work together in a structured environment.
I am still reluctant to rely completely on cooperative learning, worried that students may waist or misuse the time I give them. But if I find a structure I like, similar to the way the author of the article did, and it yields good results, than I would integrate that system more and more into my classroom as my comfort allows. Hopefully my first attempt will go better than I expect, then the transformation of my classroom will occur quicker, benefitting more of my students as well as myself.
Tim Hollenbeck